1 Introduction

The idea behind this thorn is to create a slim, common set of variables, parameters and scheduling groups which can then be used by different hydrodynamics codes. It should contain the common concepts of different hydrodynamics codes, but at the same time it should be as slim as possible to remain as general as possible. HydroBase should not contain the actual source code of typical routines of hydrodynamics codes, it should merely provide a common setup in which hydrodynamics codes can put their routines.

Because there exist different formulations of the hydrodynamics equations and not all of them involve concepts like conserved variabled or treat them differently, which is the reason why these variables are not defined in HydroBase but this is left to the hydrodynamics codes.

One of the advantages of such a common base is that modules of hydrodynamics codes only working with entities defined in HydroBase could be used interchangeably. Prime examples for this are initial data solvers or importers and analysis modules. Another advantage is that the format of output generated by different hydrodynamics codes in Cactus would be the same, including variable names and unit conventions, which would improve the ability to compare results of different codes directly a lot.

2 Using this Thorn

HydroBase is to be used as a central part of hydrodynamics fields just as ADMBase is used as a central part of spacetime evolution and analysis codes. HydroBase only stores variables which are common to most if not all hydrodynamics codes solving the Euler equations, the so called primitive variables. These are also the variables which are needed to couple to a spacetime solver and which are usually needed by analysis thorns. The usage of a common set of variables by different hydrodynamics codes creates the possibility to share parts of the code, e.g. initial data solvers or analysis routines.

Currently the defined primitive variables are (see [1] for details):

• rho: rest mass density \(\varrho \)

• press: pressure \(p\)

• eps: specific internal energy \(\epsilon \)

• vel[3]: contravariant fluid three velocity \(v^i\) with respect to the Eulerian observer defined as \begin {equation} v^i = \frac {u^i}{\alpha u^0} + \frac {\beta ^i}{\alpha } \end {equation} in terms of the four-velocity \(u^\mu \), lapse \(\alpha \), and shift vector \(\beta ^i\).

• Y_e: electron fraction \(Y_e\)

• temperature: temperature \(T\)

• entropy: specific entropy per particle \(s\)

• Bvec[3]: contravariant magnetic field vector defined as \begin {equation} B^i = \frac {1}{\sqrt {4\pi }} n_{\nu } F^{*\nu i} \end {equation} in terms of the dual \(F^{*\mu \nu } = \frac {1}{2}\varepsilon ^{\mu \nu \alpha \beta }F_{\alpha \beta }\) to the Faraday tensor and the unit normal of the foliation of spacetime \(n^\mu \).

HydroBase also sets up scheduling blocks that organize the main functions which modules of a hydrodynamics code may need. All of those scheduling blocks are optional, however if used, they might simplify existing codes and make them more interoperable. HydroBase itself does not schedule something inside most of the groups which it provides.

Currently the scheduling blocks are:

• Initializing the primitive variables

• Converting primitive variables to conservative variables

• Calculating the right hand side (RHS) in the method of lines (MoL)

• Setting and updating an excision mask

• Applying boundary conditions

In this way the initiation of the primitive variables, methods to recover the conservative variables, and basic atmosphere handling can be implemented in different thorns while allowing a central access point for analysis thorns.

3 Units

HydroBase does not require a specific set of units itself. However so that there are no misunderstandings between thorns a specific set of units is suggested. These units are derived from the conventions

which are commonly used in astrophysics and in relativity. The former sets the mass scale to the solar one and the latter adopts the same units for time, length and mass.

We assume the following definitions and constants of nature:

This corresponds to the following units for mass, length, time, and magnetic field:

Inserting the SI units into the above unit correspondences, we find the following conversion factors:

where T (Tesla) is the magnetic field unit in SI, \(1\,\mathrm {T}=1\,\mathrm {N/(A\cdot m)}\), and G (Gauss) is its cgs equivalent, \(1\,\mathrm {Tesla} = 10^4\,\mathrm {Gauss}\).

4 Acknowledgments

This thorn was produced by Tanja Bode, Roland Haas, Frank Löffler, and Erik Schnetter.

References

5 Parameters

6 Interfaces

General

Implements:

hydrobase

Inherits:

initbase

Grid Variables

6.0.1 PUBLIC GROUPS

Adds header:

HydroBase.h

Uses header:

HydroBase.h

7 Schedule

This section lists all the variables which are assigned storage by thorn EinsteinBase/HydroBase. Storage can either last for the duration of the run (Always means that if this thorn is activated storage will be assigned, Conditional means that if this thorn is activated storage will be assigned for the duration of the run if some condition is met), or can be turned on for the duration of a schedule function.

Storage

Scheduled Functions

CCTK_INITIAL (conditional)

  hydrobase_initial

  hydrobase initial data group

CCTK_STARTUP (conditional)

  hydrobase_startup

  startup banner

CCTK_INITIAL (conditional)

  hydrobase_prim2coninitial

  recover the conservative variables from the primitive variables

HydroBase_Initial (conditional)

  hydrobase_zero

  set up vacuum hydro initial data

HydroBase_Initial (conditional)

  hydrobase_y_e_one

  set electron fraction to 1

HydroBase_Initial (conditional)

  hydrobase_bvec_zero

  set magnetic field to 0

HydroBase_Initial (conditional)

  hydrobase_avec_zero

  set vector potential to 0

HydroBase_Initial (conditional)

  hydrobase_aphi_zero

  set vector potential phi to 0

HydroBase_Initial (conditional)

  hydrobase_excisionmasksetup

  set up hydro excision mask

CCTK_POSTREGRIDINITIAL (conditional)

  hydrobase_excisionmasksetup

  set up hydro excision mask

CCTK_POSTREGRID (conditional)

  hydrobase_excisionmasksetup

  set up hydro excision mask

CCTK_POST_RECOVER_VARIABLES (conditional)

  hydrobase_excisionmasksetup

  set up hydro excision mask

CCTK_PARAMCHECK (conditional)

  hydrobase_paramcheck

  check that hydrobase parameters are consistent

HydroBase_ExcisionMaskSetup (conditional)

  hydrobase_initexcisionmask

  initialize hydro excision mask to ’no excision everywhere’

CCTK_POSTSTEP (conditional)

  hydrobase_excisionhasbeenset

  group to schedule thorns changing the mask before and thorns using the mask after

MoL_CalcRHS (conditional)

  hydrobase_rhs

  groups for scheduling tasks for calculating rhs of hydro variables

MoL_PostStep (conditional)

  hydrobase_poststep

  post step tasks for hydro thorns

HydroBase_PostStep (conditional)

  hydrobase_boundaries

  hydrobase-internal boundary conditions group

HydroBase_Boundaries (conditional)

  hydrobase_select_boundaries

  group to schedule the boundary condition functions

HydroBase_Boundaries (conditional)

  applybcs

  apply the boundary conditions of hydrobase

HydroBase_PostStep (conditional)

  hydrobase_con2prim

  convert from conservative to primitive variables

CCTK_POSTPOSTINITIAL (conditional)

  hydrobase_con2prim

  convert from conservative to primitive variables (might be redundant)

Aliased Functions